The population growth of a state since 2000 in millions of people is represented by a linear model. Using the trend line, y=0.83x+30

Question

, predict the population, y
, in the year 2030. Let x=30
because the year 2030 is 30 years after the year 2000.(1 point)
Responses

In 2030, the population of the state will be 30.03 million people.
In 2030, the population of the state will be 30.03 million people.

In 2030, the population of the state will be 0.83 million people.
In 2030, the population of the state will be 0.83 million people.

In 2030, the population of the state will be 60.83 million people.
In 2030, the population of the state will be 60.83 million people.

In 2030, the population of the state will be 54.9 million people.

Answer 1

To predict the population in 2030 using the linear model \( y = 0.83x + 30 \), where \( x \) represents the number of years since 2000, we set \( x = 30 \) for the year 2030.

Now we can substitute \( x = 30 \) into the equation:

\[ y = 0.83(30) + 30 \]

Calculating this step by step:

1. First calculate \( 0.83 \times 30 \): \[ 0.83 \times 30 = 24.9 \]

2. Then, add 30: \[ y = 24.9 + 30 = 54.9 \]

So, according to the model, the predicted population in 2030 will be:

In 2030, the population of the state will be 54.9 million people.

Thus, the correct response is:

In 2030, the population of the state will be 54.9 million people.